The leg of a right-angled triangle is 8 less than the hypotenuse, and the other leg is 20

The leg of a right-angled triangle is 8 less than the hypotenuse, and the other leg is 20. Find the perimeter of the triangle.

Let the hypotenuse in a given triangle be determined through the variable a.

Then, in accordance with the conditions of this task, it will be possible to represent the unknown leg using the expression a – 8.

But after all, from the condition we know what the other side is equal to, so we can write down the equation and find out what the other 2 sides are equal to:

a ^ 2 = (a – 8) ^ 2 + 20 ^ 2;

a ^ 2 = a ^ 2 – 16a + 64 + 400;

16a = 464;

a = 29;

29 – 8 = 21.

Therefore, the perimeter of this triangle is:

29 + 21 + 20 = 70.

Answer: 70.